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由EDFA放大的脉冲激光信号作为初始脉冲信号,可以表示为:
$$ E(t) = {E_0}\exp i\left[ {\dfrac{{2\pi c}}{\lambda }t + {\varphi _0}} \right] $$ (1) 式中:t为时间;c为光速;λ为示中光纤中传输的中心波长;E0为放大后的激光脉冲光强;φ0为初始相位。
当待测区域中P点位置(如图1所示)受到了外界的干扰,则其散射信号的相位产生偏移,则在P点位置对应的tp时刻上,测试所得光强信号为:
$$ E({t_p}) = {E_p}\exp i\left[ {\dfrac{{2\pi c}}{\lambda }{t_p} + {\varphi _p}} \right] $$ (2) 式中:Ep为P点上的激光脉冲光强值;φ0为初始相位;其他参数同上。设光开关的延迟为Tswitch,则采用光纤延长线的长度L=c·Tswitch,由此可以使光纤1的初始光信号与光纤2的初始光信号在到达测试位置上的时间同步,从而为差分同源振动事件提供参考信号[14]。由此可知,将原信号光强能量归一化后可以得到其相关系数:
$$ {\rho _{12}} = \dfrac{{\int_{{{ - }}\infty }^{{{ + }}\infty } {{E_1}\left(t \right){E_2}\left(t \right){\rm{d}}t} }}{{\sqrt {\int_{{{ - }}\infty }^{{{ + }}\infty } {E_1^2\left(t \right){\rm{d}}t} } \sqrt {\int_{{{ - }}\infty }^{{{ + }}\infty } {E_2^2\left(t \right){\rm{d}}t} } }} $$ (3) 式中:E1和E2分别表示光纤1和光纤2的激光回波信号强度。又因为初始信号被声光调制为脉冲信号,即可以采用离散信号表达方式,故其表示可写为:
$$ {\rho _{12}} = \dfrac{{n\displaystyle \sum {{E_1}{E_2}} - \displaystyle \sum {{E_1}} \displaystyle \sum {{E_2}} }}{{\sqrt {n\displaystyle \sum {E_1^2} - {{\left({\displaystyle \sum {{E_1}} } \right)}^2}} \sqrt {n\displaystyle \sum {E_2^2} - {{\left({\displaystyle \sum {{E_2}} } \right)}^2}} }} $$ (4) 式中:n表示采样点数;E1和E2分别表示光纤1与光纤2上在相应点位上的光强测试值。通常情况下,相关函数的时延会影响信号相关程度的计算,但在该系统硬件设计中由于采用了延时线与光开关配合使用,所以信号之间的时延可以忽略。对两个信号进行卷积分析有:
$$ \left\{ \begin{gathered} {E_1}\left(\tau \right)×{E_2}\left(\tau \right) = \int\limits_{ - \infty }^{ + \infty } {{E_1}\left(t \right){E_2}\left({\tau - t} \right){\rm{d}}t} \\ {R_{12}}\left(\tau \right) = \int\limits_{ - \infty }^{ + \infty } {{E_1}\left(t \right){E_2}\left({\tau + t} \right){\rm{d}}t} \\ \end{gathered} \right. $$ (5) 式中:τ为时间常数;R12为光纤1与光纤2之间的自相关值。由此可得到该信号的自相关函数与自能量谱密度为傅氏变换关系。所以,对两组函数做相关运算后,再通过傅里叶变换就能完成信号的提取。
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与传统的神经网络不同,虽然原始数据都是光纤传感的回波信号,但是同一点的测试数据是由两根光纤构成的,而两个光纤的感知系数不同,故输入数据需要分组,且隐藏层设置了相关运算,从而构成了深度神经网络结构,见图2。第一隐藏层由光纤1和光纤2的测试数据分别完成初级滤波与信号匹配;再进入第二隐藏层,即相关计算层,将双数组输入的信息进行相关处理;最终经过相关运算进行信号增强的数据进入隐藏层的第三层分类层,从而实现相关信号对入侵事件类型与程度的映射,完成最终的识别输出。
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根据深度神经网络的结构设计,其程序流程如图3所示。
算法实现主要分为三个部分:第一,完成光纤1和光纤2的数据采集,并分别输入深度神经网络的第一层隐藏层,根据两条光纤不同封装方式的敏感系数进行匹配滤波,从而完成对初始数据的参数配置;第二,将经过预处理后的两组数据输入第二层隐藏层(相关计算层),完成两组数据的相关计算,依据相关计算得到的数据间的相关系数重新构建信号数组;第三,通过引入已知振动数据源(该数据源是预先采用已知事件的信号,通过网络学习得到的参数分布关系,该参数关系作为第三层隐藏层的控制条件嵌入在神经网络中),构建测试集,训练回波光谱分布数据与入侵事件类型的映射函数模型。
Optical fiber sensing recognition algorithm based on deep neural network
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摘要: 为解决光纤传感过程中不同类型事件信号混叠造成识别概率降低的问题,搭建了一种采用差分相关计算的双光纤传感结构,并在此基础上提出了基于深度神经网络的信号识别算法。首先利用双光纤回波信号计算相关系数,再通过不同事件类型信号特征设置阈值范围,从而通过相关计算与阈值滤波提高信噪比。设计了包含三个隐藏层的深度神经网络模型,以分离输入层与相关运算层的形式完成低频噪声抑制与信号混叠解调的目的。实验分别对三种常见入侵事件进行测试,并在此基础上分析了不同算法对组合事件的识别概率。结果显示三种事件的回波谱形具有显著特征。三种算法对单一触发事件的识别概率均在95%以上,该算法的识别均值为98.5%。当两个事件同时触发时,三种算法的平均识别概率分别为73.4%、 84.5%和96.4%。当三个事件同时触发时,三种算法的平均识别概率分别为65.2%、78.3%和93.5%。可见,该算法在光纤传感中信号存在干扰及混叠时具有更好的识别效果。Abstract: In order to solve the problem of reducing the recognition probability caused by the aliasing of different types of event signals in the optical fiber sensing process, a dual optical fiber sensing structure using differential correlation calculation is built. On this basis, a signal recognition algorithm based on deep neural network is proposed. First, the echo signal of the dual fiber is used to calculate the correlation coefficient. Then, the threshold range is set by signal characteristics of different event types, so as to improve the signal-to-noise ratio through correlation calculation and threshold filtering. A deep neural network model with three hidden layers is designed, and the purpose of low-frequency noise suppression and signal aliasing demodulation is accomplished by separating the input layer and the related operation layer. The experiments separately test three common intrusion events. The recognition probability of combined events by different algorithms is analyzed. The results show that the echo spectrum shape of the three events has significant characteristics. The recognition probability of the three algorithms is more than 95% for a single trigger event, and the average recognition value of this algorithm is 98.5%. When two events are triggered at the same time, the average recognition probabilities of the three algorithms are 73.4%, 84.5%, and 96.4%, respectively. When three events are triggered at the same time, the average recognition probabilities of the three algorithms are 65.2%, 78.3%, and 93.5%, respectively. It can be seen that this algorithm has a better recognition effect when there is interference and aliasing of signals in optical fiber sensing.
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